Question

Which term of the progression `10, 9 1/3, 8 2/3,...` is the first negative term?

Answer 1

Given:

`10, 9 1/3, 8 2/3,...`

First, write terms in improper fractions:

`10 = 30/3, 9 1/3 = 28/3, 8 2/3 = 26/3`

First term a = `30/3 = 10`

d = `28/3 - 30/3`

= `-2/3`

T_n​ = a + (n − 1)d

`T_n​ = 10 + (n − 1)(-2/3)`

The first negative term occurs when T_n​ < 0

`10 - 2/3(n - 1) < 0`

Multiply both sides by 3:

30 − 2(n − 1) < 0

30 − 2n + 2 < 0

32 − 2n < 0

2n > 32

⇒ n >16

The smallest whole number greater than 16 is 17.

The 17th term is the first negative term of the progression.